Most chargers made since about 2005 charge both NiMH and NiCd batteries. But some newer chargers charge only NiMH, not NiCd.
Any NiMH charger will charge both regular NiMH batteries and LSD NiMH's (Low Self Discharge NiMH).
Old NiCd chargers can't tell when to stop charging a NiMH battery
Use a smart charger! Smart chargers charge each battery separately, giving each one exactly as much energy as it needs and stops charging once it is full.
If your NiMH charger manages each cell separately, you can mix NiMh and NiCD, different sizes, and semi-fresh and nearly dead batteries at the same time. If it doesn't you can't. If you insist on mixing them anyway, some of your batteries will be undercharged and some will be overcharged.
NiZn batteries require a special charger. NiMH and NiCd chargers will not work.